This is an announcement for the paper "Free Banach spaces and the approximation properties" by Gilles Godefroy and Narutaka Ozawa.

Abstract: We characterize the metric spaces whose free space has the bounded approximation property through a Lipschitz analogue of the local reflexivity principle. We show that there exist compact metric spaces whose free spaces fail the approximation property.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46B28, 46B50

Remarks: 7 pages

Submitted from: narutaka@kurims.kyoto-u.ac.jp

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1201.0847

or

http://arXiv.org/abs/1201.0847